They might be riven with injuries, friendless with punters and without their best player for the first two matches but, according to the chair of the Royal Statistical Society's sports section, England fans should not be surprised if their team reaches the Euro 2012 semi‑finals – where they could be beaten by Germany.
After running a million computer simulations of the tournament, Dr Ian McHale, a senior lecturer in statistics at Salford University, says the data suggests that England are the third best team at the championship – behind Spain and Germany – and that they will face Ireland in the quarter-finals before losing to Germany. France and Italy, meanwhile, are statistically unlikely to get out of the group stages.
For those sceptical of his findings, McHale points out that his model predicted that Spain would win the 2010 World Cup. "The maths doesn't say that England will definitely reach the semi-final," he says, "but it does suggest that supporters should not be so pessimistic about England's chances. The analysis suggest there is a 68% chance England will get out of their group and will do better than we all expect."
To make his calculations, McHale used a two-stage process – modelling the results of individual matches based on the last 11,000 international games using an "ordered probit" model that estimates the probability of the three outcomes of a match – ie win, draw or loss – before using computers to simulate a huge number of tournaments.
The result is a clinical mathematical breakdown of the chance each team has of winning Euro 2012, without whims, prejudices or sudden fancies.
"One of my students has written a programme that goes through the Fifa website and scrapes all results," explains McHale. "From this raw data I have built a model that estimates the probability of winning a match as a function of a number of variables – including the ranking difference between two teams, home advantage, the distance a team has travelled to a match, number of goals scored, the seriousness of a game, recent results, and more.
"This results in an analysis that is much more in-depth and nuanced than basing predictions on something like the Fifa rankings, which can be a little bit dodgy when predicting match results because, as my research shows, Fifa artificially rate Middle Eastern countries higher than they should do."
Then comes the second stage – simulating the matches throughout the tournament a million times. "So let's say it's England v France, and the data suggests the chances of England winning are 40%, with the draw 30% and France 30%. The simulation will generate a random number between 0 and 1. If that number is between zero and 0.4 the computer says England win the match. If it's between 0.41 and 0.70 it says the match would be a draw. And if it is between 0.71 and 1 it says France wins. The computer then plays the whole tournament like this from the first group game to the final. Then it starts another tournament. And it does it a million times."
The results are surprising. According to the bookmakers, the 3-1 favourites Spain have an implied 25% chance of winning the tournament, but McHale's data suggests it should be more like 12%. And England, who are 14-1 with the bookies, implying a 7% chance of glory at Poland-Ukraine, actually have more like a 10% chance. So is he advocating the nation rushes to place their mortgages on Roy Hodgson's side? "Well, the data doesn't account for injuries or suspensions so it is not perfect," admits McHale. "But it does suggest that, for the first time this century, England have a better chance of winning a tournament than the bookies' odds imply."
guardian.co.uk © Guardian News and Media Limited 2010